Measuring resonance and the speed of sound: Resonance Tube
Standing Waves A standing wave is a pattern produced in a medium when a wave of particular vibrational frequencies causes reflected waves from one end of the medium to interfere with incident waves from the source. They are called standing wave patterns because specific points along the medium appear to be standing still (Figure 1). The specific frequencies that cause standing waves to be produced are known as harmonics. If the frequency of the wave does not correspond to one of these harmonics, the interference results in a disturbance in the medium that is irregular and non-repeating. Standing Waves in Resonance Tubes In this experiment we will be producing standing waves in a tube. A long tube will be submerged to a certain distance in water so that when a vibrating tuning fork is placed above the opening, a distinct sound is produced (Figure 2). You will know when resonance is found since a sudden increase in the intensity of the sound will be heard when the length of the tube out of the water is adjusted to the correct length. The surface of the water acts to reflect the sound wave back up the tube, creating the standing wave and also produces conditions for a node (a point of zero amplitude) since the air is not free to move longitudinally. The open end of the tube provides conditions for an anti-node (a point of maximum amplitude). Because of these restrictions to the top and bottom of the tube, only odd harmonics can be produced. The lengths of the tube outside the water that correspond to these odd harmonics are given by: L=\frac{n\lambda}{4} Where n is an odd integer corresponding to a specific harmonic. By rearranging this equation for the wavelength \lambda and substituting it into the equation v=f\lambda which was derived in the introduction, we find a relationship between the speed of sound in the tube and the length of the tube above the water for a given harmonic: v=\frac{4fL}{n} Unfortunately this equation is not perfect. The anti-node that we assumed to be at the top of the tube is actually found a distance above the top of the tube given by 0.3 multiplied the diameter of the tube. This small correction allows us to calculate the speed of sound even more accurately using the corrected equation: v=\frac{4f}{n}(L+0.3D) Where D is the diameter of the tube used. Experimental Procedure To observe resonance you will need a tall beaker or container filled with water, a hollow tube as long as is available, a range of tuning forks, and a metre ruler (Figure 3). This is easiest with at least two people per experimental set up. You will be moving the tube up out of the water (the lower open end still submerged), listening for an audible increase in volume of the tuning fork (see below for video examples), and then measuring the length of tube that is not submerged. Ideally your teacher may be able to provide the equipment necessary for this experiment. As mentioned in the Resonance section, systems undergoing free oscillations do so at their natural frequency; the tuning forks' natural frequency should be marked on each of them. Before you begin, you should draw up a table to write your results into; this should include a column for the frequency of the tuning fork used, and at least two columns for repeat values to be taken for improved accuracy; below is an example of the table headings you could use. As shown in Figure 2, the hollow tube should be placed in the water container vertically, and the ringing tuning fork will be held just above the open end of the hollow tube. Take measurements of the diameter of the hollow tube, once set up you are now ready to perform the experiment. If possible strike the tuning fork on rubber, as other materials such as metal or wood may produce other frequencies within the tuning forks' sound other than its natural frequency. Method: # Measure and record the diameter of the tube. # Fill the beaker almost to the top with water and place the hollow tube inside. # Ring the tuning fork on a rubber block. # Hold the ringing fork above the tube. # Move both the tuning fork and tube up until the volume of the tuning fork is increased. # Measure the height of the tube above the water at the point at which the volume is greatest. Here it is easiest if one person holds the tube in place while the other measures the height. # Once one resonant point has been measured, continue raising the tube to look for/measure more resonance points until you reach the end of the tube and it comes out of the water. # Repeat the measurements two more times and calculate an average to get more accurate results. # Repeat the method for the other tuning forks of different frequencies. # Use the values obtained and the equation for the speed of sound in a resonance tube to calculate the speed of sound. You may only find one resonant point in the tube for a particular tuning fork, typically the higher frequencies have more resonant heights for a particular length of tube. Here is an example of a table for recording measurements: Video examples of resonance points using a 1024 Hz tuning fork: